Senate Democrats and progressive activists on Friday celebrated the nomination of Judge Ketanji Brown Jackson to the Supreme Court while Republicans promised an exhaustive though respectful review of the first Black woman put forward for a seat on the high court.

“It’s critical that any such nominee, including Judge Jackson, receive the most thorough and rigorous vetting,” Senator Charles E. Grassley of Iowa, the senior Republican on the Judiciary Committee, said in a statement. “Our review will be as fair and respectful as it is complete and comprehensive.”

Democrats and their liberal allies portrayed Judge Jackson, a federal judge since 2013, as an impeccable pick for the court who would provide valuable experience as a former public defender and, in the words of Senator Chuck Schumer, the New York Democrat and majority leader, by “ensuring the Supreme Court reflects the nation as a whole.”

“To be the first to make history in our nation, you need to have an exceptional life story,” said Senator Richard J. Durbin, Democrat of Illinois, who as chairman of the Judiciary Committee will preside over confirmation hearings expected in late March. “Judge Jackson’s achievements are well known to the Senate Judiciary Committee, as we approved her to the D.C. Circuit less than a year ago with bipartisan support.”

All 50 Senate Democrats voted for Judge Jackson when she was confirmed to the U.S. Court of Appeals for the District of Columbia Circuit in June, and that same support would be enough to install her on the Supreme Court. The chief question is whether she can draw any Republican backing, and how intensely the party intends to fight the choice.

In his statement, Senator Mitch McConnell, the Kentucky Republican and minority leader, noted that he had opposed Judge Jackson last year and called her “the favored choice of far-left dark-money groups that have spent years attacking the legitimacy and structure of the court itself.”

But he and many other Republicans were uncharacteristically muted in their criticism of Judge Jackson, reflecting the party’s concern about appearing overly aggressive in attacking the first Black woman chosen to sit on the nation’s highest court.

“With that said, I look forward to carefully reviewing Judge Jackson’s nomination during the vigorous and thorough Senate process that the American people deserve,” Mr. McConnell said.

Other Republicans focused on the timeline, with Senator John Barrasso of Wyoming, the No. 3 Senate Republican, saying that “it is critical that the Senate takes all the time it needs to thoroughly evaluate Judge Jackson’s record and past decisions.”

Republicans seemed intent on making clear that they would treat Judge Jackson with respect and conduct dignified proceedings, even though most are likely to oppose her elevation to the high court. They said they were determined not to emulate the tactics of Democrats, who they contend were unfair to Justice Brett M. Kavanaugh during his confirmation hearing in 2018, when they aired allegations of past sexual misconduct.

“No matter what,” said Senator John Cornyn, Republican of Texas and a senior member of the Judiciary Committee, “Judge Jackson will be given the dignity and respect she deserves. The American people will see a starkly different process from the treatment of Justice Kavanaugh and other judicial nominees during the previous administration.”

Left unmentioned was the treatment by Republicans of Merrick B. Garland, President Barack Obama’s 2016 pick for the Supreme Court, whose nomination they blockaded for months, never holding a hearing and ultimately killing it.

This time, some Republicans suggested they would not try to stall the nomination, such as by boycotting hearings. Mr. Grassley said he had “no intention of degrading the advice and consent role as Senate Democrats have in recent confirmations. I intend to show up and do the job that Iowans pay me to do.”

Democrats cheered the nomination and promised swift confirmation.

“I know Judge Jackson will be an excellent Supreme Court justice,” said Senator Debbie Stabenow, Democrat of Michigan. “What an exciting time for our country.”

Brian Fallon, the executive director of the advocacy group Demand Justice, said Judge Jackson was a “slam-dunk” choice.

“Judge Jackson’s extraordinary breadth of experience at all levels of the judiciary, including on the nation’s second-highest court, will make her one of the most qualified nominees ever,” he said.

Zinelle October, the executive vice president of the American Constitution Society, a leading progressive advocacy group, said the nomination had special resonance for her.

“As an American, a lawyer and a Black woman, I am especially proud of this nomination,” she said. “Seeing someone who looks like me put forth for the highest court of this nation is long overdue.”